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Proof step 67 from proof inv-allocate (previous step)

jvalid1 ↔ true, err = err0, gstore = gstore3, jro0 = jro, nx0 = nx, remove-refsize0(gstore2) = gstore2, elems nx ∩ jro = ∅, dom gstore2 ∪ elems nx = dom gstore ∪ jro, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro, n0 < LEB_SIZE, n0 < jmaxino, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(gstore \ jro), inv(gstore2), inv(gstore3 \ jro), inv(gstore3[nx.last]), refsize-cons(gstore2, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), valid-journal-head(nx, gstore3, jro), nx.last ∈ gstore3, pmaxino ≤ jmaxino1, jmaxino ≤ LEB_SIZE, fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪skip⟫ ( (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi2.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi2) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore3 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore3 = ∅ ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore3 ↓) ∧ nodes(gstore ↓, jro) = nodes(gstore3 ↓, jro0) ∧ (err = ESUCCESS → jvalid1 ∧ nx ≠ [])), err = ESUCCESS, nx = [], pmaxino = 0, dups(nx)

Heuristic symbolic execution applied rule skip right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ ns ⊆ ns; (s)% ⊦ ns \ ns = ∅; (s)% ⊦ ns ∩ ∅ = ∅; (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]